Comments for MEDB 5501, Week 8
Review two-sample t-test
\(H_0:\ \mu_1=\mu_2\)
\(H_1:\ \mu_1 \ne \mu_2\)
Or a one tailed alternative
\(T=\frac{\bar X_1-\bar X_2}{SE(\bar X_1-\bar X_2)}\)
Accept H0 if T is close to zero.
What to do with three or more groups?
\(H_0:\ \mu_1=\mu_2=...=\mu_k\)
\(H_1:\ \mu_i \ne \mu_j\)
for some i, j
Note: one-tailed test is tricky.
Accept H0 if the F ratio (defined below) is close to 1.
Artificial data
g y 1 1 23 2 1 30 3 1 25 4 2 33 5 2 36 6 2 41 7 2 37 8 2 43 9 3 24 10 3 29 11 3 31
Scatterplot
Total SS = 452
Within SS = 116
Between SS = 336
Degrees of freedom
For Total SS, df = 10
For Within SS, df = 8
For Between SS, df = 2
In general,
N = number of observations
k = number of groups
Total df = N-1
Within df = N-k
Between df = k-1
ANOVA table, 1 of 4
ANOVA table, 2 of 4
ANOVA table, 3 of 4
ANOVA table, 4 of 4
ANOVA table from the general linear model
YRBSS analysis
YRBSS analysis
YRBSS analysis
YRBSS analysis
YRBSS analysis
YRBSS analysis
YRBSS analysis
YRBSS analysis
YRBSS analysis
YRBSS analysis
YRBSS analysis
YRBSS analysis
YRBSS analysis
YRBSS analysis
YRBSS analysis
YRBSS analysis
YRBSS analysis
YRBSS analysis
YRBSS analysis
YRBSS analysis
